Singular Integral Equations of Convolution Type with Reflection and Translation Shifts. (4th July 2019)

• Record Type: Journal Article
• Authors: Li, Pingrun
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 9(2019)
• Page Start: 1023
• Page End: 1038
• Publication Date: 2019-07-04
• Subjects: Singular integral equations of convolution type -- Riemann boundary value problems -- integral operators -- reflection -- translation shift; 45E10 -- 45E05 -- 30E25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1586721
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This article deals with some kinds of singular integral equations of convolution type with reflection in class {0}. Such equations are transformed into the Riemann boundary value problems with both discontinuous coefficients and reflection by Fourier transform. For such problems, we propose one method different from classical one, by which the explicit solutions and the conditions of solvability are obtained. Finally, we propose and discuss singular integral equations with reflection and translation shifts.